For given functions f1,...,fn : R → R consider the optimization problem Prove: If x¯ = (x¯1,..., x¯n) is a minimal solution of this problem and for every i ∈ {1,...,n} the function fi is...

For given functions f1,...,fn : R → R consider the optimization problem

Prove: If x¯ = (x¯1,..., x¯n) is a minimal solution of this problem and for every i ∈ {1,...,n} the function fi is differentiable at x¯i, then there is a real number α with